MADRID — Maria Menendez, a 25-year-old caught in Spain’s job-destroying economic crisis, would love to work in Germany as a veterinarian. Germany, facing an acute shortage of skilled workers, would love to have her.

The European Union was built on a grand vision of free labor markets in which talent could be matched with demand in a seamless and efficient manner, much in the way workers in the United States hop across states in search of opportunity. But today only 3 percent of working age EU citizens live in a different EU country, research shows. As young people in crisis-hit southern Europe face unemployment rates hovering at 50 percent, many find themselves caught in a language trap, unable to communicate in the powerhouse economy that needs their skills the most: Germany.

‘‘I think going abroad is my best option,’’ said Menendez, ‘‘but for people like me who have never studied German, it would be like starting from zero.’’

In northern Europe, companies are desperately seeking to plug labor gaps caused by low birth rates and the growing need for specialized skills amid still robust economies. Germany alone requires tens of thousands of engineers, IT specialists, nurses, and doctors to keep its economy thriving in the years to come.

But a recent study pinpointed language as the single biggest barrier to cross-border mobility in Europe.

‘‘What seems to prevent further labor market integration in Europe is the fact that we speak different languages,’’ said Nicola Fuchs-Schuendeln, a Frankfurt University economics professor who coauthored the study.

Few German employers are prepared to compromise when it comes to language skills, according to Raimund Becker, who heads the German Federal Employment Agency’s division for foreign and specialist recruitment. ‘‘If you want to work as an engineer, you’ll need a certain specialist vocabulary,’’ he said. ‘‘Even colloquial German isn’t enough.’’

Earlier this year the agency announced it would invest up to $51 million in special programs to help jobless Europeans aged 18 and 35 learn German.

The measure targets people like Menendez, who graduated from veterinary school and has two master’s degrees but hasn’t been able to find work in Spain.

Menendez said she found plenty of jobs online in Germany, where EU rules mean her Spanish qualification would be accepted. But the ads are either in German or, if in English, say that candidates must have good German.

Like most Spaniards, she studied English at school and is now focusing on improving her English. Often touted as the continent’s “lingua franca,” English is widely used in multinational companies but rarely in the public sector or the small- to medium-sized enterprises that employ the bulk of the European labor force. Meanwhile, London isn’t the magnet for young English-speaking Europeans that it used to be. Migrants who flocked there a decade ago are now returning home or looking elsewhere for work as Britain, too, struggles with a rising jobless rate.

Ricardo de Campano, 34, learned the hard way how critical it is to have a wide set of language skills when he left London for Berlin two years ago. He said he quickly found work as a special needs teacher in London with the English he’d learned at school, but the same wasn’t true when he came to Germany.

De Campano is now studying German at an adult education college where Spaniards have come to make up the biggest single group of students in recent years.

Despite the boom in German language teaching seen also in Spain itself, the number of Spaniards coming to Germany remains modest. According to figures from the Federal Employment Agency, less than 5,000 Spaniards have taken up jobs in Germany over the past year — a tiny fraction of the 4.7 million jobless in Spain.

Ten years ago, European leaders at a meeting in Barcelona called for ‘‘action to improve the mastery of basic skills, in particular by teaching at least two foreign languages from a very early age.’’ Six years later, the EU’s language czar, Leonard Orban, declared that speaking two foreign languages in addition to their mother tongue should be the goal for all citizens of the 27-nation bloc.

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